What is the solution to the system of equations?

3 x minus 4 y = 16. 2 x + 3 y = 5.

(a) The derivative of the function, dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)

(b) The equation of the tangent line to the curve at (1, 1) is y = (-779/9)x + 778/9.

To find dy/dx, we differentiate both sides of the equation with respect to x using the chain rule and product rule as necessary:

d/dx (57x⁷) + d/dx (10x³⁸y) + d/dx (y⁹) = d/dx (68)

Simplifying each term using the power rule and the chain rule where appropriate, we get:

399x⁶ + 380x³⁷y + 9y⁸(dy/dx) = 0

Now, solving for dy/dx, we get:

dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)

To find the equation of the tangent line to the curve at (1, 1), we first need to evaluate dy/dx at that point. Plugging in x = 1 and y = 1 into the expression for dy/dx, we get:

dy/dx = (-399 - 380) / 9 = -779/9

Now we can use the point-slope form of the equation of a line to find the tangent line. The point-slope form is:

y - y1 = m(x - x1)

where;

Plugging in m = -779/9, x1 = 1, and y1 = 1, we get:

y - 1 = (-779/9)(x - 1)

Simplifying, we get:

y = (-779/9)x + 778/9

Learn more about equation of tangent line here: https://brainly.com/question/28199103

#SPJ1

The electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.

What is an electric field?

An electric field is a region in which an electric charge experiences a force. It is created by an electric charge or a changing magnetic field. Electric fields exist everywhere in nature and are vital to the functioning of many electronic devices. Electric fields are also used to describe the motion of electrons in a conductor and the behavior of electric currents.

The electric field at the origin (x=0, y=0) can be calculated using the equation of electric field,

E = k(q1/r1² + q2/r2²)

Where k is the Coulomb's constant, q1 and q2 are the charges and r1 and r2 are the distances from the charges to the origin.

The electric field at the origin can be calculated by substituting the given values in the equation.

The distance from the charge at y = 4.0 cm to the origin is 5 cm and the distance from the charge at y = -4.0 cm to the origin is also 5 cm.

E = 8.988 X 10⁹ (3.8 X 10⁻⁹/25 + 3.8 X 10⁻⁹/25)

E = 8.99 X 10⁹ (3.8 X 10⁻⁹/25)

E = 1.05 X 10⁷ N/C

Therefore, the electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.

For more questions related to Coulomb's constant

brainly.com/question/30196309

#SPJ9

Right Question:-

Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y, Find electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm?

Answer:

If the new cereal box contains 20% more than the original cereal box, then the original cereal box contained 100% - 20% = 80% of the new cereal box.

Let X be the original cereal box amount in ounces, then we can set up the following equation:

X + 0.20X = 18.48

Simplifying and solving for X:

1.20X = 18.48

X = 15.40

Therefore, the original cereal box amount was 15.40 ounces.

Step-by-step explanation:

therefore 9 x 9+12

81+144

225/2

15

Therefore, the option D is correct [tex]\frac{4dollar}{1lb}[/tex]

The rate of change of a linear function is the slope of the line, which represents the rate at which the output (dependent variable) changes with respect to the input (independent variable).

A line's slope is calculated by dividing the difference in y-coordinates between any two locations on the line by the difference in x-coordinates. Geometrically, the slope is the tangent of the angle that the line makes with the x-axis.

Here in the graph we have x and y values find out the slope,

To calculate the slope of a line from two points (x1, y1) and (x2, y2), we use the formula:

[tex]Slope =\frac{(y2 - y1)}{(x2 - x1)}[/tex] = 4 (for every two points)

So, the line is linear and the rate of change of this linear function is 4/1, which means that for every 1 lb increase in the x-coordinate, the y-coordinate (the output) increases by $4.

Therefor the option D is correct [tex]\frac{4dollar}{1lb}[/tex]

To know more about slope, visit:

https://brainly.com/question/16949303

#SPJ1

hi!

first, you have to graph the piecewise function. a piecewise function is basically where there are multiple different lines, but they all have different sections on the graph that they are applicable.

on the graph, graph the first equation, in the piecewise function, which is y= -3x + 2.

then, you have to erase all parts except the segment between x=-1 and x=1. at the endpoints, place a filled in dot to mark the point.

do the same with y = x - 2, however, this time, the restraints are at x=1 and x=3. you'll see that the endpoint at x=1 coincides with the previous equation! for the endpoint on the side of x=3, you should place another filled in dot to mark that it includes x=3.

i've attatched a screenshot below (scroll down a bit!) of what the graph should look like, in case that was confusing :)

next, you can fill in the table by finding what the function outputs for the given x. for the first one, x = -3. first, look at the function. is x between -1 and 1, or between 1 and 3? neither. that means that it is no solution for that point.

continue down the table. it is the same with x=-2.

next, x = -1. this is in the interval of -1<=x<=1, so you should look at the first equation in the piecewise function, which is 2-3x. if we plug in -1 for x, we get 2 - 3(-1) = 2+3 = 5. this means that the point is (-1, 5). you should make sure that this is a point that you plotted on the graph, and if not, the graph is wrong :(

continue down the table and keep doing that!

next question is if there is a min or max. there is! as you can see, the piecewise function only goes from x=-1 through x=3, and all other values give a no solution output. so, the minimum is -1 and the maximum is 3.

next: turning point or vertex. this would be at the point when x = 1, since that would be where the graph changes direction. the vertex is at (1, -1).

the zeroes of the function is where the graph crosses the x-axis. this means that y=0. we can see that this happens when x=2/3 and when x=2.

i hope this was helpful! :)

The value for the x in the triangle with sides  (4x - 4) and 30 is obtained as x > 6.8.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Assume that the side length 30 is the greatest of the 3 sides.

Using this fact, we can write an inequality based on the lengths of the sides in the given triangle -

(4x - 4) + x > 30

Simplifying this inequality, we get -

4x + x - 4 > 30

Adding x on LHS, we get -

5x > 34

Dividing both sides by 5, we get -

x > 6.8

Therefore, the value of x is greater than 6.8.

To learn more about triangles from the given link

https://brainly.com/question/25215131

#SPJ1

the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued

The answer if subpart are as follows :-

A) To find the annual rate of change between 1991 and 2000, we need to use the formula for exponential decay, which is:

V(t) = V(0) * e raise to the power (-rt)

Where V(t) is the value of the car at time t, V(0) is the initial value of the car, r is the annual rate of change (as a decimal), and e is the mathematical constant 2.71828...

Plugging in the values we have:

V(2000) = $12,000

V(1991) = $45,000

t = 9 years

$12,000 = $45,000 * e raise to the power (-r * 9)

Dividing both sides by $45,000 and taking the natural logarithm of both sides gives:

ln(0.26667) = -9r

Solving for r:

r = ln(0.26667) / (-9) = 0.1356

So the annual rate of change between 1991 and 2000 is 0.1356, which represents a decrease in value of 13.56% per year.

B) To express the answer from part A in percentage form, we need to multiply by 100 and round to two decimal places:

r = 0.1356 * 100 = 13.56%

C) If we assume that the car value continues to drop by the same percentage as it did between 1991 and 2000, we can use the same formula as before to find the value of the car in 2003:

V(2003) = V(2000) * e raise to the power (-r * 3)

Plugging in the values we have:

r = 0.1356

V(2000) = $12,000

V(2003) = $12,000 * e raise to the power (-0.1356 * 3) = $6,044.48

So the value of the car in 2003 would be approximately $6,044.48, rounded to the nearest 50 dollars as requested.

In summary, the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued. It's worth noting that this calculation is based on the assumption of exponential decay, which may not accurately model the actual depreciation of a car over time.

To know more about interest visit :-

https://brainly.com/question/25793394

#SPJ1

Answer:

38

Step-by-step explanation:

Let x represent the number of days Timmy has been driving his car since he had 3,000 miles on it. Then, his total mileage can be represented as:

Total mileage = 3,000 + (38 × x)

This is a linear model, because the relationship between the total mileage and the number of days driven is a straight line with a constant slope of 38. The y-intercept of this line is 3,000, which represents the initial mileage on Timmy's car. The slope of 38 indicates that the car is being driven 38 miles further each day, which corresponds to the rate of change in the total mileage.

Answer:13)2,4,6,8

14)x=3

Step-by-step explanation:

13) you should make it equal to numbers inside bracket {}.

for example,

1.-6x+11=-37

-6x=-37-11=-48

x=8

2.-6x+11=-25

-6x=-36

x=6

3.-6x+11=-13

-6x=-24

x=4

4.-6x+11=-1

-6x=-12

x=2

14)f(x)=13

f(x)=3x+4=13

3x=9

x=3

Using the graph the value of the function (f + g)(-2) = 5

A graph is a diagrammatic representation of a function

Since we have the graphs of the function f(x) and g(x), we desire to find (f + g)(-2). We proceed as follows.

First, we note that (f + g)(x) = f(x) + g(x)

Now, we need to find (f + g)(-2) = f(-2) + g(-2)

So, we use the graph to find these values.

From the graph

f(-2) = 2 and g(-2) = 3

So, substituting the values of the variables into the equation, we have that

(f + g)(-2) = f(-2) + g(-2)

= 2 + 3

= 5

So, (f + g)(-2) = 5

Learn more about graphs here:

https://brainly.com/question/24748644

#SPJ1

Answer:

See below.

Step-by-step explanation:

We are asked to round 4.586 cm to the nearest cm.

Rounding is a simple method used to change a number, and all of the numbers behind it to 0. Rounding is similar to an approximation, in order to show you how I should give you an example.

Example:

Round 459 to the hundreds place.

The hundreds place is where the 4 is. We should look at the 5.

Requirements necessary are that 5 needs to be greater than [tex]4.\bar{9}.[/tex]

Because 5 is greater, we can round up to 500.

Rounding is an approximation because it's close to the actual number, in other words, inexact.

Let's use the example as a guide for our problem now.

4.586 to the nearest cm (ones place)

The ones place is the 4. We should look at the 5.

5 is greater than [tex]4.\bar{9}.[/tex]

Because 5 is greater, we can round up to 5.000 cm.

Our final answer is 5.000 cm.

Answer:

0

Step-by-step explanation:

3r-9=3(r+3)

3r-9=3r+9

collect like terms

3r-3r=9-9

r=0

Answer:

[tex]\large\boxed{\textsf{No Solutions.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identify how many solutions are possible for r.}[/tex]

[tex]\textsf{First, we should simplify the given equation.}[/tex]

[tex]\textsf{For one part of the equation, we have to use the \underline{Distributive Property}.}[/tex]

[tex]\Large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\textsf{The \underline{Distributive Property} is a property used to distribute the \underline{multiplier} into}[/tex]

[tex]\textsf{values \underline{inside} the parentheses.}[/tex]

[tex]\textsf{Let's begin simplifying the equation.}[/tex]

[tex]\large\underline{\textsf{Simplify.}}[/tex]

[tex]\mathtt{3r-9=3(r+3)}[/tex]

[tex]\large\underline{\textsf{Distribute:}}[/tex]

[tex]\mathtt{3r-9=(3 \times r)+(3 \times 3)}[/tex]

[tex]\mathtt{3r-9=3r+9}[/tex]

[tex]\large\boxed{\textsf{No Solutions.}}[/tex]

[tex]\large\underline{\textsf{Why?:}}[/tex]

[tex]\textsf{Any value that is substituted into r will \underline{never} make the equation true.}[/tex]

Answer: whole = 45; part = 15%

Step-by-step explanation:

The part ( a.k.a the fraction) is the percentage.

15% can be expressed as 15/100 = 3/20.

The whole is 45.

Hope this helps! :)

Using percentage, we can get that 7ml of the 70% solution will be needed.

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form.

In this context, "%" is read as "percent" or "percentage" to represent a percentage. By "division by 100," the percent symbol can always be changed to a fraction or decimal equivalent.

In the given question we get the equation,

35(245) + 0.75x = 0.4(245+x) = 98 + 0.4x

85.75 + 0.75x = 98 + 0.4x

0.35x = 98-85.75 = 12.25

x = 12.25/.35 = 35 mL of 75% solution

mixed with 245 mL of 35% it yields 280 mL of 40% so,

35 is within 5 of 40

75 is within 35 of 40

35/5 = 7

245/35 = 7

To know more about percentages, visit:

https://brainly.com/question/30348137

#SPJ1

The bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.

First, we need tο calculate the amοunt οf DDE in the 200g οf seal that the bald eagle eats:

If a delay differential equatiοn (DDE) equilibrium is lοcally asymptοtically stable fοr all delays, it is said tο be tοtally stable. We οutline standards fοr DDEs with discrete time delays' absοlute stability.

Calculate the amοunt οf DDE in 1 gram οf fish:

1.0 micrοgram οf DDE per gram οf fish

Calculate the amοunt οf fish the seal eats tο accumulate 2.0 micrοgrams οf DDE in its tissue:

2.0 micrοgrams οf DDE per gram οf seal / 1.0 micrοgram οf DDE per gram οf fish = 2.0 grams οf fish per gram οf seal

Calculate the amοunt οf seal that the bald eagle eats:

200g οf seal

Calculate the amοunt οf fish the bald eagle cοnsumes frοm the 200g οf seal:

200g οf seal * (1 gram οf fish / 2.0 grams οf fish per gram οf seal) = 100g οf fish

Calculate the amοunt οf DDE the bald eagle cοnsumes frοm the fish it ate frοm the seal:

100g οf fish * 1.0 micrοgram οf DDE per gram οf fish = 100 micrοgrams οf DDE

Therefοre, the bald eagle cοnsumes 100 micrοgrams οf DDE in οne day.

Learn more about DDE
https://brainly.com/question/1507612

#SPJ1

That note about "both signs have been reversed" only applies to the example on the right side, where –4 was distributed into the expression in parentheses.

Notice on the left example, the signs were not reversed.

When you distribute a negative number, that's when the signs will reverse.  Since you're distributing a negative number, you'll be multiplying each term in parentheses by a negative number and that negative is what reverses the sign on every term.

So, yes all of the signs will be reversed each time you distribute a negative number into the parentheses, but not if you distribute a positive number.

Answer:

For the lifetime membership to be cheaper than paying $550 in annual membership dues, we need to calculate the present value of the lifetime membership and compare it to the present value of the stream of annual payments.

The present value of the lifetime membership can be calculated using the formula for the present value of a lump sum:

PV = FV / (1 + r)^n

where FV is the future value (which is the cost of the lifetime membership today, $5,000), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.

The present value of the stream of annual payments can be calculated using the formula for the present value of an annuity:

PV = A * [(1 - (1 + r)^-n) / r]

where A is the annual payment ($550), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.

We need to find the minimum number of years for which the present value of the lifetime membership is less than the present value of the stream of annual payments. We can do this by setting the two present values equal to each other and solving for n:

5000 / (1 + 0.075)^n = 550 * [(1 - (1 + 0.075)^-n) / 0.075]

Solving this equation gives n ≈ 18.7 years. Rounded up to the nearest year, this means that Lloyd must remain a member of the ADLA for at least 19 years for the lifetime membership to be cheaper than paying $550 in annual membership dues.

Therefore, the answer is 19 years.

For the second question, we can use the formula for the future value of a lump sum:

FV = PV * (1 + r)^n

where PV is the present value ($24), r is the annual interest rate (4.5%), and n is the number of years (392).

Substituting the given values, we get:

FV = 24 * (1 + 0.045)^392

FV ≈ $859,993,041.68

Therefore, the value of the $24 purchase price as of 2018 is approximately $859,993,041.68.

g-1(x) = ex - 1 is the inverse οf the functiοn g(x) = lοg(x + 1) as taking away 1 frοm bοth sides .

A functiοn is a mathematical fοrmula that gives each input value in a set an individual οutput value. Tο put it anοther way, a functiοn is a cοnnectiοn between twο sets where each element in the first set (referred tο as the dοmain). There are several methοds tο express a functiοn, including with a graph, a table οf values, οr a fοrmula. Mοst frequently, a fοrmula οr equatiοn is used tο represent a functiοn.

We need tο sοlve fοr x in terms οf g in οrder tο derive the inverse functiοn g-1(x) οf g(x) = lοg(x + 1). (x).

We can expοnentiate bοth sides by starting with g(x) = lοg(x + 1) and using the definitiοn οf lοgarithms:

G(x) = lοg(x + 1) = e(x)

[tex]e^{(g(x))} = x + 1[/tex]

Hence, by taking away 1 frοm bοth sides, we can isοlate x:

[tex]x = e^{(g(x))} - 1[/tex]

Inverse functiοn g-1(x) is thus:

[tex]g-1(x) = e^x - 1[/tex]

Hence, g-1(x) = ex - 1 is the inverse οf the functiοn g(x) = lοg(x + 1) as taking away 1 frοm bοth sides .

To know more about function visit:

brainly.com/question/28193995

#SPJ1

Probability of rolling a number greater than 0 but less than 7 is 1.

The probability formula is as follows:

Probability = Favourable outcomes / Total outcomes

Sample space of rolling a dice:

S = {1, 2, 3, 4, 5, 6}

Total outcomes = 6

Favourable outcomes: number greater than 0 but less than 7

Favourable outcomes: 6

Then, probability of rolling a number greater than 0 but less than 7

Probability = Favourable outcomes / Total outcomes

Probability = 6/6

Probability = 1

Thus,  probability of rolling a number greater than 0 but less than 7 is 1.

Know more about probability

https://brainly.com/question/24756209

#SPJ9

The complete question is-

A dice is being rolled. Find the probability of rolling a number greater than 0 but less than 7

One possible solution of this system is Arun has 5 nickels and 15 pennies.

One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system.

x+y≥20

0.05x+0.01y≤0.40

x≥0

y≥0

Inequality: y≥20-x

Inequality: y≥5x-40

x≥0

y≥0

The solution set satisfying the inequality is shown in black area above when x=5 and y=15

So, Arun has 5 nickels and 15 pennies.

Graph of the system of inequalities is attached below.

To know more about variables, visit:

https://brainly.com/question/15078630

#SPJ9

Answer:

79 degrees

Step-by-step explanation:

[tex]x + y = 90 \: degrees \\ 11 + y = 90 \\ y = 90 - 11 \\ y = 79 \: degrees[/tex]

Answer:

x=3

Step-by-step explanation

x=7 is an excluded value for the quotient x=3 because 3 is not an integer.

The correct side lengths to complete the table are RS: Geometric mean of PR and QR, PR: Geometric mean of RS and QR and QR: Geometric mean of PR and RS.

Geometric is a branch of mathematics that focuses on the study of shapes, sizes, and relative positions of figures and the properties that are derived from them. It is a type of mathematics that is used to describe the properties of objects and their relationships to one another in space. Geometry is also used to describe the movement of objects in space.

The side lengths of right triangle PQR are:
PR: The length of side PR is the geometric mean of RS and QR.
QR: The length of side QR is the geometric mean of PR and RS.
RS: The length of side RS is the geometric mean of PR and QR.
PQ: The length of side PQ is the hypotenuse of the right triangle PQR.
PS: The length of side PS is the hypotenuse of the right triangle PSR.
QS: The length of side QS is the hypotenuse of the right triangle QSR.

Therefore, the correct side lengths to complete the table are:
RS: Geometric mean of PR and QR
PR: Geometric mean of RS and QR
QR: Geometric mean of PR and RS.

To learn more about Geometric
https://brainly.com/question/24643676
#SPJ1

Answer:

The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth

Step-by-step explanation:

The total area of earth covered by water is about 350,000,000 km². This represents about 70% of earths total surface area. What is the approximate total surface area of earth

True, The polynomial 32x^2+12x-57 has two real roots.

What is a polynomial, exactly?

A polynomial in mathematics is an expression that consists of variables (also known as indeterminates) and coefficients and uses only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

                             The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

It is an absolutely true statement that the polynomial 32x^2+12x-57 has two real roots. The correct option among all the options that are given in the question is the first option or option "A".

Learn more about polynomial

brainly.com/question/11536910

#SPJ9

The complete question is -

The polynomial 32x^2+12x-57 has two real roots.

A. True

B. False The polynomial 32x^2+12x-57 has two real roots.

Answer:

5/12

Step-by-step explanation:

3/4 - 1/3

We need to use the common denominator of 12

3/4 * 3/3 = 9/12

1/3 * 4/4 = 4/12

9/12 - 4/12 = 5/12

Using the data points given, the equation is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].

What is an ellipse?

An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).

We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).

We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.

Therefore, we have -

a = 9 - 4 = 5

Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -

c = distance from (4,-2) to (4,3)

c = [tex]\sqrt{((4-4)^2 + (3-(-2))^2}[/tex]

c = 5

Now, we can use the equation of an ellipse -

[tex]\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1[/tex]

where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.

Plugging in the values we have found, we get -

[tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex]

Therefore, the equation for the ellipse is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].

To learn more about ellipse from the given link

https://brainly.com/question/9702250

#SPJ1

Answer:

Step-by-step explanation:

about 18.7

Answer:

18.7

Step-by-step explanation:

2 gray cars / 15 cars = x gray cars / 140 cars

Solving for x, we get:

x = 2 gray cars * 140 cars / 15 cars

x = 18.67 gray cars